This phrase doesn't specify an exact time period, just that it's longer than very soon. The museum will be under renovation for the foreseeable future.
Pro Tip 2/3
Vague Duration
Use when the exact duration is unknown, but expected to be long. She'll be working abroad for the foreseeable future.
Pro Tip 3/3
Expectation
Implies an expectation based on current information or trends. With the current budget cuts, funding will be limited for the foreseeable future.